(this is a reprise of a previous post)

Revised to yield a unique answer!

Sorry to all who already dug in

Three perfectly logical prisoners are seated facing each other, with hats on their heads. Each hat has a counting number {1, 2, 3, 4, …} on it, and each prisoner can see the hat of the other two prisoners, but not his own.

The warden says, “I will set free the man who can tell me his own number, but execute any man guessing incorrectly.

They look back at him in stunned silence.

OK, a hint. One of your numbers is the sum of the two. Alan?”
— “I don’t know my number.
Bert?
— “I don’t know my number.
Graham?
— “I don’t know my number.
Alan?
— “I still don’t know my number.
Bert?
— “My number is 78 26.

And he went free. What were Alan and Graham’s numbers? (And how did you discover this?)

1. February 19, 2008 am29 2:58 am 2:58 am

Are all three numbers necessarily different?

2. February 19, 2008 am29 3:01 am 3:01 am

It’s not specified.

3. February 25, 2008 pm29 7:34 pm 7:34 pm

isabel on colored hats,
a few days later at GPD.

4. February 25, 2008 pm29 7:35 pm 7:35 pm

gaah! that link should’ve been this one!